Units, estimation and rounding

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शिक्षकों के लिए: Units, estimation and rounding (Mathematics, Number) के लिए इस्तेमाल के लिए तैयार लेसन स्लाइड्स, रिवीज़न नोट्स — इन्हें अपने लेसन में इस्तेमाल करें, या टॉपिक को एक इंटरैक्टिव क्लास एक्टिविटी की तरह चलाएं जिसे आपके शिक्षार्थी लाइव गेम की तरह खेलें।

लेसन नोट्स स्लाइड्स प्रैक्टिस सवाल

लेसन नोट्स

Rounding

Decimal places (d.p.) count digits after the decimal point; significant figures (s.f.) count from the first non-zero digit.
Look at the next digit: 5 or more rounds up. 3.4567 to 2 d.p. = 3.46; 0.004567 to 2 s.f. = 0.0046.
Zeros matter: 0.0500 to 3 s.f. keeps the trailing zeros to show precision.

Estimation

Round each number to 1 significant figure and calculate: \frac{39.2 \times 4.8}{0.52}\approx \frac{40 \times 5}{0.5} = 400.
For a quotient with positive inputs, increasing the numerator and decreasing a positive denominator gives an overestimate. If some changes increase and others decrease the result, inspect the effect rather than guessing.

Standard form

Write numbers as A \times 10ⁿ where 1 \leq A < 10. 45\,000 = 4.5 \times 10⁴; 0.0032 = 3.2 \times 10^-3.
Multiply: multiply the As and add the powers. Divide: divide the As and subtract powers. Adjust A if it leaves the range.

Units and approximations

Always give units. Round at the end, not during a calculation.
Use \approx for approximate equality, and the correct number of significant figures for the data given.

Length, area and volume units

Error intervals

Rounded values give an error interval: 4.6 to 1 d.p. means 4.55 \leq x < 4.65.

Values rounding to 4.6

स्लाइड्स

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साइन अप करें — फ्री लॉग इन

प्रैक्टिस सवाल

फ्री प्रीव्यू — 32 में से 8 सवाल। सभी देखने के लिए साइन अप करें।

1.Round 7.8 to the nearest whole number.
Easy
- A7
- B8
- C9
- D7.5
2.Round 4.567 to 1 decimal place.
Easy
- A4.5
- B4.6
- C4.57
- D4.0
3.Round 3482 to 2 significant figures.
Easy
- A3500
- B3400
- C3480
- D3490
4.Round 0.004567 to 2 significant figures.
Easy
- A0.0045
- B0.0046
- C0.005
- D0.00457
5.Round 12.95 to 1 decimal place.
Easy
- A12.9
- B13.0
- C12.95
- D12.0
6.Estimate 19.8 \times 5.1 by rounding to 1 s.f.
Easy
- A100
- B90
- C120
- D80
7.Write 45 000 in standard form.
Easy
- A4.5 \times 10⁴
- B45 \times 10³
- C4.5 \times 10³
- D0.45 \times 10⁵
8.Write 0.0032 in standard form.
Easy
- A3.2 \times 10^-3
- B3.2 \times 10³
- C32 \times 10^-4
- D3.2 \times 10^-2

और सवाल

9.What is 6.5 \times 10³ as an ordinary number?
Easy
- A650
- B6500
- C65 000
- D0.0065
10.Estimate (39.2 × 4.8)/0.52 by rounding each input to 1 significant figure.
Medium
- A400
- B40
- C4000
- D360
11.Calculate (3 \times 10⁴) \times (2 \times 10³).
Medium
- A6 \times 10⁷
- B6 \times 10¹²
- C5 \times 10⁷
- D6 \times 10¹
12.Calculate (8 \times 10⁶) \div (2 \times 10²).
Medium
- A4 \times 10⁴
- B4 \times 10⁸
- C16 \times 10⁴
- D4 \times 10³
13.Calculate (6 \times 10⁵) \times (5 \times 10⁴) in standard form.
Medium
- A3 \times 10¹⁰
- B30 \times 10⁹
- C3 \times 10⁹
- D11 \times 10⁹
14.Which is the largest?
Medium
- A3.2 \times 10⁴
- B5.1 \times 10³
- C9.9 \times 10³
- D1.2 \times 10⁴
15.A number rounded to 1 d.p. is 4.6. What is its error interval?
Medium
- A4.55 \leq x < 4.65
- B4.5 \leq x < 4.7
- C4.6 \leq x < 4.7
- D4.55 \leq x \leq 4.65
16.How many significant figures does 0.00402 have?
Medium
- A3
- B5
- C6
- D2
17.\frac{4.8 \times 10^-3}{1.2 \times 10²} equals:
Medium
- A4 \times 10^-5
- B4 \times 10^-1
- C5.76 \times 10^-1
- D4 \times 10⁵
18.Calculate (2.5 \times 10⁴) + (3 \times 10³) in standard form.
Medium
- A2.8 \times 10⁴
- B5.5 \times 10⁷
- C2.8 \times 10⁷
- D5.5 \times 10⁴
19.Estimate \frac{58 \times 102}{0.48} by rounding each number to 1 significant figure.
Medium
- A12 000
- B1200
- C120 000
- D6000
20.Which has more significant figures: 0.0450 or 4.5?
Easy
- A0.0450
- B4.5
- Cthe same
- Dcannot tell
21.When an accurate final result is required in a multi-step calculation, when should you round to the requested precision?
Easy
- Aat the end
- Bat every step
- Cat the beginning
- Dnever
22.Which number rounds to 5.2 to 1 decimal place?
Medium
- A5.14
- B5.17
- C5.25
- D5.3
23.In 0.0046 the leading zeros are significant.
Easy
True or false?
24.4.5 \times 10⁴ equals 45 000.
Easy
True or false?
25.42 \times 10³ is written in standard form.
Easy
True or false?
26.Rounding inputs to 1 significant figure is one useful way to make an estimate.
Easy
True or false?
27.A value rounded to 1 d.p. as 4.6 could be 4.64.
Medium
True or false?
28.Which numbers are in standard form?
Medium
- A3.5 \times 10⁶
- B35 \times 10⁵
- C9.99 \times 10^-2
- D0.5 \times 10³
- E1 \times 10⁰
29.Which round to 3.5 to 1 d.p.?
Medium
- A3.46
- B3.54
- C3.55
- D3.449
- E3.51
30.Round 6.049 to 2 decimal places.
Easy
- A6.04
- B6.05
- C6.0
- D6.1
31.Round 0.0830 to 1 significant figure.
Easy
- A0.08
- B0.09
- C0.1
- D0.083
32.Write (3.6 \times 10⁵) \div (1.2 \times 10²) in standard form and show your working.
Medium

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