Decimals: tenths and hundredths

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Apuntes de la lección

What is a decimal?

A decimal is a way to write numbers that are not whole, using a decimal point (.) to separate the whole part from the fraction part.
The decimal point is like a separator: numbers to the left are whole numbers, numbers to the right are parts of a whole.
In the number 3.7, the 3 is the whole part and the 7 is the fraction part.
Decimals are based on tenths and hundredths. The first digit after the point is tenths, the second is hundredths.
Example: In 0.5, the 5 is in the tenths place, so 0.5 means 5 tenths.

Tenths and hundredths as fractions

One tenth is written as 0.1 and as a fraction it is \frac{1}{10} .
One hundredth is written as 0.01 and as a fraction it is \frac{1}{100} .
The number 0.25 means 25 hundredths, which is the same as \frac{25}{100} .
You can write tenths as hundredths: 0.3 = 0.30, because 3 tenths = 30 hundredths.
Remember: 10 hundredths make 1 tenth, and 100 hundredths make 1 whole.

Place value after the decimal point

The first digit after the decimal point is in the tenths place.
The second digit after the decimal point is in the hundredths place.
In 0.47, the 4 is in the tenths place (4 tenths) and the 7 is in the hundredths place (7 hundredths).
The value of a digit depends on its place: in 0.62, the 6 is worth 6 tenths (0.6) and the 2 is worth 2 hundredths (0.02).
You can read 0.47 as 'four tenths and seven hundredths' or 'forty-seven hundredths'.

Comparing and ordering decimals

To compare decimals, look at the digits from left to right, starting with the whole number part.
If the whole parts are equal, compare the tenths digit. If those are equal, compare the hundredths digit.
Example: 0.5 is greater than 0.3 because 5 tenths is more than 3 tenths.
Example: 0.42 is less than 0.47 because they have the same tenths (4) but 2 hundredths is less than 7 hundredths.
You can also compare by thinking of fractions: 0.6 = 6/10 and 0.59 = 59/100, so 0.6 is greater because 60/100 > 59/100.

Decimals on a number line

You can place decimals on a number line between whole numbers.
The space between 0 and 1 can be divided into 10 equal parts for tenths.
Each tenth can be divided into 10 smaller parts for hundredths.
Example: 0.3 is three tenths of the way from 0 to 1.
Example: 0.25 is two tenths and five hundredths, which is a quarter of the way from 0 to 1.

Rounding decimals to the nearest whole number

Rounding means finding the closest whole number to a decimal.
Look at the digit in the tenths place. If it is 5 or more, round up. If it is 4 or less, round down.
Example: 3.7 rounds to 4 because the tenths digit is 7 (≥5).
Example: 3.4 rounds to 3 because the tenths digit is 4 (<5).
If the tenths digit is exactly 5, round up: 2.5 rounds to 3.

Decimals in money and measurement

Money uses decimals: £1.50 means 1 pound and 50 pence.
There are 100 pence in a pound, so 0.01 of a pound is 1 penny.
Measurements use decimals: 1.5 metres means 1 metre and 50 centimetres.
There are 100 centimetres in a metre, so 0.01 of a metre is 1 centimetre.
When solving problems with money or measurements, write the decimal correctly and use the units.

Equivalent decimals

Equivalent decimals are decimals that have the same value but look different.
Adding zeros at the end of a decimal does not change its value: 0.5 = 0.50 = 0.500.
Removing trailing zeros also does not change the value: 0.70 = 0.7.
This works because 0.5 is 5 tenths, and 0.50 is 50 hundredths, which is the same amount.
When comparing decimals, you can add zeros to make them have the same number of digits.

Writing fractions as decimals

Any fraction with denominator 10 or 100 can be written as a decimal.
For tenths: the numerator goes in the tenths place. Example: \frac{3}{10} = 0.3.
For hundredths: the numerator goes in the hundredths place. Example: \frac{25}{100} = 0.25.
If a fraction has denominator 10, you can write it as hundredths by multiplying top and bottom by 10: \frac{3}{10} = \frac{30}{100} = 0.30.
Practice: \frac{7}{10} = 0.7, \frac{9}{100} = 0.09.

Solving simple problems with decimals

Add and subtract decimals by lining up the decimal points.
Example: 0.4 + 0.3 = 0.7 because 4 tenths + 3 tenths = 7 tenths.
Example: 0.45 + 0.20 = 0.65 because 45 hundredths + 20 hundredths = 65 hundredths.
When adding or subtracting money, keep the pounds and pence separate: £2.50 + £1.25 = £3.75.
Check your answer by estimating with whole numbers.

Diapositivas

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Preguntas de práctica

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1.What is the decimal for the fraction 1/10?
Easy
- A0.1
- B0.01
- C1.0
- D10.0
2.What is the decimal for the fraction 25/100?
Easy
- A0.25
- B2.5
- C0.025
- D25.0
3.The decimal 0.3 is equal to the fraction 3/10.
Easy
True or false?
4.Order these decimals from smallest to largest: 0.3, 0.12, 0.25.
Easy
- 0.3
- 0.12
- 0.25
5.Which decimal is greater: 0.5 or 0.05?
Medium
- A0.5
- B0.05
- CThey are equal
- DCannot tell
6.The decimal 0.20 is equal to 0.2.
Medium
True or false?
7.Which of the following is the correct way to write 35 hundredths as a decimal?
Medium
- A0.35
- B3.5
- C0.035
- D35.0
8.Which of the following decimals are less than 0.5? (select all that apply)
Medium
- A0.45
- B0.55
- C0.09
- D0.5
- E0.3

Más preguntas

9.Match each fraction to its decimal equivalent.
Medium
- 1/10
- 3/100
- 7/10
- 0.1
- 0.03
- 0.7
10.Put these decimals in order from smallest to largest: 0.09, 0.1, 0.9, 0.19
Medium
- 0.09
- 0.1
- 0.9
- 0.19
11.Which of the following decimals are equal to 0.5? (select all that apply)
Medium
- A0.50
- B0.05
- C5/10
- D50/100
- E0.15
12.The decimal 0.7 is greater than 0.07.
Easy
True or false?
13.Which number is the smallest?
Medium
- A0.32
- B0.4
- C0.09
- D0.25
14.Match each decimal to its place value of the digit 5.
Medium
- 0.5
- 0.05
- 0.15
- 0.55
- 5 tenths
- 5 hundredths
- 5 hundredths
- 5 tenths and 5 hundredths
15.Arrange these decimals from largest to smallest: 0.45, 0.5, 0.09, 0.4
Medium
- 0.45
- 0.5
- 0.09
- 0.4
16.Which of the following are true? (select all that apply)
Medium
- A0.6 > 0.06
- B0.3 = 0.30
- C0.8 < 0.08
- D0.5 = 5/100
17.The number 0.25 is equal to 25/100.
Easy
True or false?
18.Which digit is in the tenths place in the decimal 0.47?
Easy
- A4
- B7
- C0
- D47
19.What is 0.8 written as a fraction in simplest form?
Easy
- A\frac{8}{10}
- B\frac{4}{5}
- C\frac{8}{100}
- D\frac{4}{10}
20.Which decimal is equal to \frac{7}{100}?
Medium
- A0.7
- B0.07
- C0.007
- D7.0
21.Which of the following are equal to 0.30? (select all that apply)
Medium
- A0.3
- B0.03
- C\frac{30}{100}
- D0.300
- E3 tenths
22.The decimal 0.5 is greater than 0.50.
Easy
True or false?
23.Put these decimals in order from smallest to largest: 0.45, 0.4, 0.54, 0.5
Medium
- 0.45
- 0.4
- 0.54
- 0.5
24.Which of the following is the correct way to write 8 hundredths as a decimal?
Medium
- A0.8
- B0.08
- C0.008
- D8.0
25.0.4 is less than 0.39.
Easy
True or false?
26.Which decimal is greater than 0.6 but less than 0.7?
Medium
- A0.58
- B0.63
- C0.72
- D0.6
27.0.07 is greater than 0.1.
Medium
True or false?
28.A rope is cut into 4 equal pieces. Each piece is 0.25 metres long. What was the original length of the rope in metres?
Medium
- A1.00
- B0.50
- C0.75
- D1.25
29.A cake is cut into 100 equal pieces. If you eat 0.35 of the cake, how many pieces did you eat?
Hard
- A35
- B3.5
- C350
- D0.35
30.A shop sells apples at £0.40 each. How much do 3 apples cost?
Hard
- A£1.20
- B£1.00
- C£0.43
- D£1.40
31.A jug contains 1.25 litres of juice. You pour out 0.35 litres. How much juice is left in litres?
Hard
- A0.90
- B1.60
- C0.80
- D1.10
32.A bag of flour weighs 1.5 kilograms. You use 0.75 kilograms for a recipe. How much flour is left in kilograms?
Hard
- A0.75
- B0.25
- C1.25
- D0.85
33.A bottle of juice has 0.6 litres. You drink 0.35 litres. How much juice is left in litres?
Hard
- A0.25
- B0.95
- C0.35
- D0.45
34.What does the digit 7 represent in the decimal 0.47?
Easy
- A7 tenths
- B7 hundredths
- C7 ones
- D7 tens
35.Which of the following is the correct way to write 3 tenths as a decimal?
Easy
- A0.03
- B0.3
- C3.0
- D0.30
36.The decimal 0.04 is greater than 0.4.
Easy
True or false?
37.Which of the following decimals are equal to 0.50? (Select all that apply)
Medium
- A0.5
- B0.05
- C0.500
- D5/10
- E50/100
38.Put these decimals in order from smallest to largest: 0.25, 0.5, 0.05, 0.2
Medium
- 0.25
- 0.5
- 0.05
- 0.2
39.Which decimal is greater than 0.35 but less than 0.4?
Medium
- A0.3
- B0.36
- C0.41
- D0.45
40.Match each decimal to its equivalent fraction.
Medium
- 0.4
- 0.25
- 0.75
- 25/100
- 4/10
- 75/100
41.Fill in the blank: In the decimal 0.57, the digit 5 is in the _______ place.
Easy
In the decimal 0.57, the digit 5 is in the ____ place.
42.What is 0.7 rounded to the nearest whole number?
Easy
43.A rope is 2.45 metres long. How many centimetres is that? (1 metre = 100 centimetres)
Medium
44.A pencil is 0.35 metres long. How many centimetres is that? (1 metre = 100 centimetres)
Medium
45.Write the missing decimal for each fraction.
Easy
7/10 = ____ 23/100 = ____ 9/100 = ____
46.Write the decimal shown by the shaded part of a 10x10 grid (100 squares, 37 shaded).
Medium
The shaded part represents ____
47.A ribbon is 0.65 metres long. How many centimetres is that? (1 metre = 100 centimetres)
Medium
48.Write the decimal for the fraction.
Easy
\frac{9}{10} = ____
49.What is 0.83 rounded to the nearest tenth?
Medium
50.What is the decimal for 7 tenths?
Easy
51.What is the decimal for 45 hundredths?
Easy
52.Fill in the blank:
Easy
In the decimal 0.63, the digit 6 is in the ____ place and the digit 3 is in the ____ place.
53.Explain why 0.3 and 0.30 are equal, even though they look different.
Hard
54.A number line has a point halfway between 0.4 and 0.5. What decimal does it represent? Explain your answer.
Hard
55.Explain why 0.20 and 0.2 are equal, even though they look different.
Hard
56.What is 0.7 rounded to the nearest whole number?
Easy
- A0
- B3
- C2
- D1
57.A rope is 2.45 metres long. How many centimetres is that? (1 metre = 100 centimetres)
Medium
- A245 cm
- B295 cm
- C270 cm
- D220 cm
58.A pencil is 0.35 metres long. How many centimetres is that? (1 metre = 100 centimetres)
Medium
- A35 cm
- B39 cm
- C31 cm
- D43 cm
59.A ribbon is 0.65 metres long. How many centimetres is that? (1 metre = 100 centimetres)
Medium
- A72 cm
- B58 cm
- C65 cm
- D79 cm
60.What is 0.83 rounded to the nearest tenth?
Medium
- A-0.2
- B1.8
- C2.8
- D0.8
61.What is the decimal for 7 tenths?
Easy
- A-0.3
- B2.7
- C0.7
- D1.7
62.What is the decimal for 45 hundredths?
Easy
- A2.45
- B-0.55
- C0.45
- D1.45

Apuntes de repaso

## Decimals: Tenths and Hundredths A **decimal** is a way to write numbers that are not whole, using a dot (.) called the **decimal point**. The digits after the point show parts of a whole. ### Tenths and Hundredths - **Tenths** are parts when a whole is split into 10 equal pieces. One tenth is written as 0.1 and equals 1/10. - **Hundredths** are parts when a whole is split into 100 equal pieces. One hundredth is written as 0.01 and equals 1/100. - You can write any fraction with denominator 10 or 100 as a decimal: - 3/10 = 0.3 (three tenths) - 25/100 = 0.25 (twenty-five hundredths) ### Place Value In a decimal like 0.25, each digit has a place value: - The first digit after the point is the **tenths** place. - The second digit after the point is the **hundredths** place. - So in 0.25, the 2 is 2 tenths (2/10) and the 5 is 5 hundredths (5/100). ### Comparing and Ordering To compare decimals, look at the digits from left to right. Start with the tenths place. If they are the same, look at the hundredths place. - 0.3 > 0.25 because 3 tenths is more than 2 tenths. - 0.25 = 0.250 because extra zeros at the end do not change the value. You can also use a **number line** to see which decimal is bigger. The number further to the right is greater. ### Rounding to the Nearest Whole Number To round a decimal to the nearest whole number, look at the digit in the tenths place. - If it is 5 or more, round up. - If it is 4 or less, round down. - Examples: 3.4 rounds to 3, 3.5 rounds to 4. ### Money and Measurements Decimals are used with money and measurements. - **Money**: £1.25 means 1 pound and 25 pence. 100 pence = 1 pound, so 25 pence = 0.25 pounds. - **Length**: 1 metre = 100 centimetres, so 1 cm = 0.01 m. 25 cm = 0.25 m. ### Key Facts - 0.1 = 1/10, 0.01 = 1/100 - 0.25 = 25/100 = 1/4 - Adding zeros at the end of a decimal does not change its value (0.5 = 0.50). - The decimal point separates whole numbers from parts. Practice by writing fractions as decimals, comparing decimals, and rounding them to the nearest whole number.

decimal: A number that uses a decimal point to show parts of a whole, like 0.5 or 0.25.
decimal point: The dot (.) that separates the whole number part from the fractional part in a decimal, as in 3.14.
tenths: One of ten equal parts of a whole. Written as 0.1 or 1/10.
hundredths: One of one hundred equal parts of a whole. Written as 0.01 or 1/100.
place value: The value of a digit based on its position in a number. In decimals, the first digit after the point is tenths, the second is hundredths.
compare: To decide which number is greater or smaller. For decimals, compare digits from left to right.
order: To arrange numbers from smallest to largest or largest to smallest.
number line: A line with numbers marked at equal intervals, used to show the order and value of numbers.
round: To change a number to a nearby simpler number. For example, 3.4 rounds to 3, and 3.5 rounds to 4.
pence: Small units of money in the UK. There are 100 pence in one pound.
centimetre: A unit of length. There are 100 centimetres in one metre.

Tarjetas

What is a decimal?

A decimal is a way to write numbers that are not whole, using a dot (.) called a decimal point. For example, 0.5 is a decimal.

What does the first digit after the decimal point mean?

The first digit after the decimal point is the tenths place. It tells you how many tenths (1/10) you have. For example, in 0.3, the 3 means 3 tenths.

What does the second digit after the decimal point mean?

The second digit after the decimal point is the hundredths place. It tells you how many hundredths (1/100) you have. For example, in 0.07, the 7 means 7 hundredths.

How do you write 1/10 as a decimal?

1/10 is written as 0.1. The 1 is in the tenths place.

How do you write 25/100 as a decimal?

25/100 is written as 0.25. The 2 is in the tenths place and the 5 is in the hundredths place.

What is the value of the digit 7 in 0.75?

The digit 7 is in the tenths place, so its value is 7/10 or 0.7.

What is the value of the digit 5 in 0.35?

The digit 5 is in the hundredths place, so its value is 5/100 or 0.05.

How do you read the decimal 0.4?

You read it as 'four tenths' because the 4 is in the tenths place.

How do you read the decimal 0.23?

You read it as 'twenty-three hundredths' because the digits are in the tenths and hundredths places.

What is 0.6 as a fraction?

0.6 is 6/10. You can also simplify it to 3/5, but 6/10 is correct for tenths.

What is 0.08 as a fraction?

0.08 is 8/100. You can also simplify it to 2/25, but 8/100 is correct for hundredths.

Which is bigger: 0.3 or 0.25?

0.3 is bigger because 0.3 is 3/10 (or 30/100) and 0.25 is 25/100. 30/100 is greater than 25/100.

Which is smaller: 0.7 or 0.07?

0.07 is smaller because 0.7 is 7/10 (or 70/100) and 0.07 is 7/100. 7/100 is less than 70/100.

How do you compare 0.5 and 0.50?

They are equal. 0.5 is 5/10 (or 50/100) and 0.50 is 50/100. The extra zero at the end does not change the value.

Place 0.4 on a number line between 0 and 1.

0.4 is four tenths of the way from 0 to 1. It is closer to 0 than to 1.

Place 0.75 on a number line between 0 and 1.

0.75 is seventy-five hundredths of the way from 0 to 1. It is closer to 1 than to 0.

Round 0.6 to the nearest whole number.

0.6 rounds to 1 because the tenths digit is 5 or more, so you round up.

Round 0.4 to the nearest whole number.

0.4 rounds to 0 because the tenths digit is less than 5, so you round down.

Write 3 pounds and 25 pence as a decimal in pounds.

£3.25 because 25 pence is 25/100 of a pound, which is 0.25 pounds.

Write 2 metres and 7 centimetres as a decimal in metres.

2.07 metres because 7 centimetres is 7/100 of a metre, which is 0.07 metres.

What is 0.9 as a fraction with denominator 10?

0.9 = 9/10.

What is 0.03 as a fraction with denominator 100?

0.03 = 3/100.

What is the decimal for 7/10?

0.7.

What is the decimal for 45/100?

0.45.

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