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1.3 Place Value

GCSE Maths Foundation · Edexcel · Chapter 1: Number

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: the value of a digit, ordering, rounding to 10, 100 and 1000, significant figures and estimating. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Write down the value of any digit in a whole number or a decimal
  • Put whole numbers and decimals in order of size
  • Round to the nearest 10, 100 or 1000 and to a given number of significant figures
  • Estimate answers by rounding each number to 1 significant figure

Key words

  • Place value: The value a digit has because of its position. In 352 the 5 is worth 50.
  • Significant figure (s.f.): Digits that show the size of a number. Count from the first non-zero digit.
  • Estimate: A rough answer found by rounding the numbers first.
  • Approximation: A rounded value. The symbol ≈ means “is approximately equal to”, e.g. 4.9 × 21 ≈ 100.

The value of a digit

Each column is worth ten times the column to its right. After the decimal point the columns are tenths, hundredths and thousandths.

Worked example: reading the table

In 52 306.48:
the 2 is in the thousands column, so it is worth 2000;
the 4 is in the tenths column, so it is worth 4 tenths (0.4);
the 0 is a place holder – it shows there are no tens.

Answer: 2000 and 0.4

Ordering numbers

For whole numbers, more digits means a bigger number. For decimals, line up the decimal points and compare digits from the left. Adding zeros at the end can help: 0.5 = 0.500.

Worked example: ordering decimals

Write in order, smallest first: 0.47, 0.5, 0.409, 0.45
Write each with 3 d.p.: 0.470, 0.500, 0.409, 0.450
Compare: 409 < 450 < 470 < 500

Answer: 0.409, 0.45, 0.47, 0.5

Use the symbols < (is less than) and > (is greater than): 3.08 < 3.8.

Rounding to the nearest 10, 100 or 1000

Find the two numbers it lies between, then decide which it is closer to. Look at the digit to the right of the one you are rounding to: 5 or more rounds up.

Worked example: three ways

Round 7 482 to the nearest (a) 10 (b) 100 (c) 1000
(a) between 7 480 and 7 490; units digit 2, so 7 480
(b) between 7 400 and 7 500; tens digit 8, so 7 500
(c) between 7 000 and 8 000; hundreds digit 4, so 7 000

Answer: 7 480, 7 500, 7 000

Significant figures

The first significant figure is the first digit that is not zero. Round in the same way, but keep zeros that hold the place value.

  • 48 372; 1 s.f. 50 000; 2 s.f. 48 000; 3 s.f. 48 400
  • 0.006 815; 1 s.f. 0.007; 2 s.f. 0.0068; 3 s.f. 0.006 82
  • 3.0962; 1 s.f. 3; 2 s.f. 3.1; 3 s.f. 3.10

Worked example: keeping zeros

Round 3.0962 to 3 significant figures.
The first three significant figures are 3, 0 and 9. The next digit is 6, so the 9 rounds up to 10. That gives 3.10.
Write 3.10, not 3.1, to show 3 significant figures.

Answer: 3.10

Estimating

Round every number to 1 significant figure, then do the easier calculation. Show the rounded numbers in your working.

Worked example: estimate a calculation

Estimate (612 × 4.87) ÷ 0.48
612 ≈ 600, 4.87 ≈ 5, 0.48 ≈ 0.5
600 × 5 = 3000, then 3000 ÷ 0.5 = 6000

Answer: ≈ 6000

Worked example: over or under?

Estimate 6.7 × 28.4 and say whether it is an overestimate or an underestimate.
7 × 30 = 210
Both numbers were rounded up, so 210 is an overestimate.

Answer: 210, an overestimate

Common mistakes

  • Thinking 0.45 is bigger than 0.5 because 45 is bigger than 5. Compare 0.45 with 0.50.
  • Counting the zeros at the start of a decimal as significant figures. In 0.006 815 the first significant figure is 6.
  • Leaving out place-holding zeros: 48 372 to 2 s.f. is 48 000, not 48.
  • Working out the exact answer when the question says “estimate”. Round first, then calculate.

Revision questions

Try these, then check your answers below each one.

Question 1. What is the value of the digit 4 in the number 6 248.3? (Choose from: 4, 40, 400, 4 000.)

Answer: 40

Working: The 4 is in the tens column, so its value is 40.

Question 2. Round 38 562 to the nearest 100.

Answer: 38600

Working: The tens digit is 6, so round up: 38 562 → 38 600.

Question 3. Write 0.004 917 correct to 2 significant figures.

Answer: 0.0049

Working: The first two significant figures are 4 and 9. The next digit is 1, so round down: 0.0049.

Related lessons

Continue in the full course

This lesson is section 1.3 (EGCMF0103) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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