Reading And Ordering Numbers

Place Value

• Each digit in a number has a value depending on its **position** (place).
• Each place is **ten times larger** than the place to its right.
• For whole numbers, places are: ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, etc.
• For decimals, places to the right of the decimal point are: tenths, hundredths, thousandths, etc.
• To read large numbers, group digits in threes from the right (e.g., 12 345 678 is twelve million, three hundred and forty-five thousand, six hundred and seventy-eight).
• To read decimals, say the whole number part, then "point", then each digit separately (e.g., 36.952 is thirty-six point nine five two).

Reading and Writing Numbers in Words and Figures

• To write a number in words, use place value names and commas between groups (e.g., 60 025 → sixty thousand and twenty-five).
• To write a number in figures, write digits for each place value (e.g., fifty-three thousand and thirty-five → 53 035).
• Remember to include zeros for missing place values (e.g., forty thousand three hundred → 40 300).
• Common mistakes: forgetting "and" for hundreds (e.g., 1850 → one thousand, eight hundred and fifty).

Negative Numbers

• Negative numbers are **less than zero** and are written with a minus sign (e.g., -8).
• They are read as "negative eight" or "minus eight".
• Adding a negative is the same as subtracting the positive: $7 + (-3) = 7 - 3 = 4$.
• Subtracting a negative is the same as adding the positive: $5 - (-3) = 5 + 3 = 8$.
• Multiplying or dividing two numbers with the **same sign** gives a positive result.
• Multiplying or dividing two numbers with **different signs** gives a negative result.
• Negative numbers are used in real life for **temperature** (below zero) and **debt** (money owed).

Ordering Numbers

• **Ascending order** means smallest to largest (most negative first).
• **Descending order** means largest to smallest (most positive first).
• To compare numbers, write them with the same number of decimal places and line up place-value columns.
• For negative numbers, remember that -14 is **less than** -8 (larger digit means smaller number).
• When ordering a mix of positives and negatives, order each group separately then combine (negatives first, then positives).

Working with Negative Numbers in Context

• Temperature changes: a rise of 6°C from -4°C gives 2°C; a fall of 5°C from 3°C gives -2°C.
• Difference in temperature: subtract the lower temperature from the higher (e.g., difference between -6°C and 5°C is $5 - (-6) = 11^{\circ}C)$.
• Debt: if you owe $200 and borrow $400 more, total debt is -$600 $(i.e., -200 + (-400) = -600)$.
• Paying off debt: if you owe $300 and pay $200, you now owe -$100 $(i.e., -300 + 200 = -100)$.

Common Exam Question Types

• Write a number in words (e.g., 11 678 → eleven thousand, six hundred and seventy-eight).
• Write a number in figures (e.g., six hundred and two thousand, nine hundred and ninety-five → 602 995).
• Find the value of a digit (e.g., the 7 in 570 296 is worth 70 000).
• Calculate temperature differences and changes (e.g., from -3°C to 5°C difference is 8°C).
• Order a list of numbers including decimals and negatives (e.g., -2.4, -1.05, 0.58, 1.05).

Place Value Chart for Whole Numbers

Place Value Chart for Decimals

Negative Numbers on a Number Line

Comparing Decimals