PAss Functional Skills

Place value, ordering and rounding

How to read the value of each digit, put decimals in order, round to decimal places and significant figures, and use rounding to estimate. AQA Foundation, spec reference N1, N14 and N15.
  • GCSE
  • AQA
  • Maths
  • Foundation
  • Spec N1 · N14 · N15
  • 10 min read
  • 7 revision boxes

Introduction

2 boxes
2 min read

What is place value?

Place value is the value a digit has because of where it sits in a number. The digit 7 is worth 700 in 4,712 and seven hundredths in 0.07.

The number 4,712 with each digit labelled by its column value: 4 thousands, 7 hundreds, 1 ten, 2 units

The same digit is worth a different amount in each column.
Each column to the left is ten times bigger than the one beside it, and each column to the right is ten times smaller.
3,481.26 written out

The place value table

The decimal point never moves. When you multiply or divide by 10, 100 or 1000, the digits move columns instead — ×10\times 10 moves every digit one column left, ÷10\div 10 one column right.
Thousands
Hundreds
Tens
Units
.
Tenths
Hundredths
3
4
8
1
.
2
6

Learning

2 boxes
4 steps

How to order integers and decimals

Compare column by column from the left — not by how many digits there are. 0.4 is bigger than 0.39 because 4 tenths beats 3 tenths.
  1. Line the numbers up by their decimal points.
  2. Fill any short numbers with zeros so they all have the same number of decimal places.
  3. Compare the digits column by column, starting from the left.
  4. Write your answer using the original numbers, not the filled-in versions.
Order 0.4, 0.39, 0.401, 0.09 from smallest to largest.
Fill to the same length: 0.400, 0.390, 0.401, 0.090.
Answer: 0.09, 0.39, 0.4, 0.401
3 rules

Rounding: nearest 10, decimal places and significant figures

Find the digit you are rounding to, then look at the digit immediately to its right. 5 or more rounds up; 4 or less stays as it is. For significant figures, start counting at the first non-zero digit.

  • Nearest 10, 100, 1000

    Look at the digit in the column to the right of the one you're rounding to.
    4,678 → 4,700 (nearest 100)

  • Decimal places

    Count places after the decimal point, then look at the next digit along.
    0.0472 → 0.05 (2 d.p.)

  • Significant figures

    Start at the first non-zero digit; hold place value with zeros.
    0.00385 → 0.0039 (2 s.f.)

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Examples

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2 marks · worked example

Estimate (18.7×4.2)÷0.51(18.7 \times 4.2) \div 0.51

1 mark

Write the value of the 6 in 45.62

1 mark

A crowd is 8,700 to the nearest hundred. Write the smallest possible crowd

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Common questions

What's the difference between decimal places and significant figures?
Decimal places count from the decimal point. Significant figures count from the first non-zero digit, so 0.00482 to 2 s.f. is 0.0048 but to 2 d.p. it is 0.00.
Do I round the same way if the digit is exactly 5?
Yes — at GCSE, exactly 5 rounds up. So 3.25 to 1 decimal place is 3.3.