Place Value and Decimals to Thousandths

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Place value is the idea that a digit's position decides its value. The digit 5 is worth 500 in 527, but only 5 hundredths (0.05) in 3.152. Everything in decimals — rounding, ordering, adding, multiplying — depends on this page, so learn it well.

Key words

1. The place value chart

Each column is worth 10 times the column on its right, and one tenth of the column on its left. This pattern carries on past the decimal point. Here is the number 3527.416 in a place value chart:

• 10 thousandths = 1 hundredth (10 × 0.001 = 0.01)
• 10 hundredths = 1 tenth (10 × 0.01 = 0.1)
• 10 tenths = 1 one (10 × 0.1 = 1)
• So 1 = 10 tenths = 100 hundredths = 1000 thousandths.

Reading decimals aloud. Say the digits after the point one at a time: 3.416 is "three point four one six", not "three point four hundred and sixteen". You can also say it as a fraction: 3 and 416 thousandths.

Zero as a placeholder. 0.5, 0.05 and 0.005 are very different numbers. The zeros push the 5 into the hundredths or thousandths place. Zeros at the end of a decimal do not change its value: 0.5 = 0.50 = 0.500 (5 tenths = 50 hundredths = 500 thousandths).

Decimals on a number line. Between two tenths there are ten hundredths, and between two hundredths there are ten thousandths. Zooming in on a number line shows this:

2. Multiplying and dividing by 10, 100 and 1000

When you multiply or divide by 10, 100 or 1000, the digits move and the decimal point stays where it is. The digits keep their order; only their places change.

Method (numbered steps):

1. Count the zeros: 10 → 1 place, 100 → 2 places, 1000 → 3 places.
2. Multiplying makes the number bigger, so move the digits to the left. Dividing makes it smaller, so move them to the right.
3. Fill any empty places between the digits and the point with zeros (4.65 × 1000 = 4650; 38 ÷ 1000 = 0.038).
4. Do not write zeros at the end of a decimal, or in front of a whole number: write 46.5, not 46.50, and 465, not 0465.
5. Check with a sense of size: × 1000 should give a much bigger number; ÷ 1000 a much smaller one.

Missing-number questions. If 0.62 × ☐ = 620, look at how far the digits moved: the 6 moved from tenths to hundreds, which is 3 places, so ☐ = 1000. If ☐ ÷ 100 = 0.37, undo it: 0.37 × 100 = 37.

Where you meet this: changing units. 1 m = 100 cm, so 2.35 m = 2.35 × 100 = 235 cm. 1 kg = 1000 g, so 750 g = 750 ÷ 1000 = 0.75 kg.

3. Composing, decomposing and regrouping

Decomposing means writing a number as the sum of the values of its digits:

• 6.284 = 6 + 0.2 + 0.08 + 0.004
• 40.507 = 40 + 0.5 + 0.007 (no ones and no hundredths, so there is nothing to write for them)

Composing is the reverse. Put each part in its place. Be careful when the parts are given in a mixed order: 9 + 0.03 + 0.5 = 9.53 (the 0.5 is tenths, the 0.03 is hundredths). Using a place value chart stops you writing 9.035.

Regrouping means exchanging one unit for ten of the next smaller unit (or ten for one bigger). The number stays the same — only the way we split it changes. Here are some ways to make 2.586:

Counting how many tenths, hundredths or thousandths. 2.37 = 23.7 tenths = 237 hundredths = 2370 thousandths. To find how many hundredths, multiply by 100; how many thousandths, multiply by 1000.

Worked examples

Worked example 1 — Write the value of the digit 8 in 14.386. [1 mark]

1. Name the places after the point: 3 is tenths, 8 is hundredths, 6 is thousandths.
2. 8 hundredths = 8/100 = 0.08.

Answer: 0.08 (or 8 hundredths). Common mistake: writing "8" or "hundreds". Hundreds are on the left of the point; hundredths are on the right.

Worked example 2 — Complete: (a) 0.47 × 100 = ☐ (b) 0.47 × ☐ = 470 (c) 3.9 ÷ 100 = ☐ [3 marks]

1. (a) × 100: digits move 2 places left. 4 tenths become 4 tens, 7 hundredths become 7 ones → 47.
2. (b) 0.47 → 470: the 4 moved from tenths to hundreds = 3 places → 1000.
3. (c) ÷ 100: digits move 2 places right. 3 ones become 3 hundredths → 0.039.

Common mistake: in (c), writing 0.39 (moving only one place) or 0.0039 (moving three). Count the zeros in 100: two.

Worked example 3 — Write 7.062 as the sum of the values of its digits. [1 mark]

7 is ones, 0 is tenths, 6 is hundredths, 2 is thousandths. Answer: 7 + 0.06 + 0.002. The zero tenths add nothing, so you do not need to write + 0. Common mistake: writing 7 + 0.6 + 0.2 — the 6 is hundredths, not tenths.

Worked example 4 — Complete these: (a) 5.43 = 4 + ☐ (b) 5.43 = 5 + 0.3 + ☐ [2 marks]

1. (a) Take 4 away from 5.43: 5.43 − 4 = 1.43. (One of the ones has been regrouped into the second part.)
2. (b) 5.43 = 5 + 0.43. You already have 0.3, and 0.43 − 0.3 = 0.13. (One tenth was regrouped as 10 hundredths: 0.1 + 0.03 = 0.13.)

Check: 4 + 1.43 = 5.43 ✓ and 5 + 0.3 + 0.13 = 5.43 ✓. Always add your parts back together to check.

Worked example 5 — A pack of 1000 sheets of paper is 94 mm thick. How thick is one sheet? Give your answer in mm. [1 mark]

One sheet = 94 ÷ 1000. The digits move 3 places to the right: 94 → 9.4 → 0.94 → 0.094. Answer: 0.094 mm. Check: 0.094 × 1000 = 94 ✓.

Worked example 6 — Sara says: "To multiply by 10 you just add a zero, so 2.5 × 10 = 2.50." Is she correct? Explain. [1 mark]

Answer: No. 2.50 has the same value as 2.5, so adding a zero after the decimal part changes nothing. When you multiply by 10 the digits move one place to the left: 2 ones become 2 tens and 5 tenths become 5 ones, so 2.5 × 10 = 25. ("Add a zero" only works for whole numbers, such as 25 × 10 = 250.)

Practice

All pages in this course

Start here

• Checkpoint 6 Maths: The Test and How to Prepare

Number: integers and calculation

• Counting On and Back and Negative Numbers
• Sequences, Letters and Position-to-Term Rules
• Order of Operations, Brackets and Laws of Arithmetic
• Multiplying Whole Numbers (up to 10 000 × 2-digit)
• Dividing Whole Numbers (up to 1000 ÷ 2-digit)
• Factors, Multiples and Tests of Divisibility
• Square Numbers and Cube Numbers

Number: place value, decimals, fractions, percentages and ratio

• Place Value and Decimals to Thousandths
• Rounding Decimals
• Fractions: Division, Operators and Simplest Form
• Adding and Subtracting Fractions
• Multiplying and Dividing Fractions by Whole Numbers
• Fractions, Decimals and Percentages: Equivalence and Ordering
• Adding, Subtracting, Multiplying and Dividing Decimals
• Ratio and Direct Proportion

Geometry and measure

• Time: Decimals and Mixed Units
• Quadrilaterals: Properties and Classification
• Circles: Parts and Constructing Circles
• Angles: Measuring, Drawing and Angles in a Triangle
• Area of Rectangles and Right-angled Triangles
• 3D Shapes, Compound Shapes and Nets
• Capacity, Volume and Surface Area
• Coordinates in Four Quadrants
• Rotational Symmetry, Translation, Reflection and Rotation

Statistics and probability

• Collecting and Representing Data
• Mode, Median, Mean and Range, and Interpreting Data
• Probability

Practice tests

• Checkpoint 6 Maths — Practice Test 1
• Checkpoint 6 Maths — Practice Test 2
• Checkpoint 6 Maths — Practice Test 3