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Foundations · Numbers

Place value, rounding and estimation

Reading big numbers digit by digit, rounding to any place, and estimating an answer before you calculate it.

First, the rules

Every digit has a place, and the place is its value

The same digit 7 means seven, seventy or seven thousand depending on where it stands. Once you can read places, rounding and estimating are one glance each.

★ Places
Example 1
… thousands · hundreds · tens · units . tenths · hundredths · thousandths …
Each place is worth ten times the one to its right.
Expanded form
Example 1
4 837 = 4000 + 800 + 30 + 7
2.56 = 2 + 0.5 + 0.06
Comparing
Line up the places and compare from the left: 3 412 > 3 389 because 4 hundreds beat 3 hundreds.
★ Rounding
Example 2
Find the place you keep. Look at the next digit: 5 or more → round up, 4 or less → keep. Everything after becomes 0 (or disappears after the point).
Significant figures
Example 2
Count from the first non-zero digit. 0.00482 to 2 s.f. is 0.0048; 48 371 to 1 s.f. is 50 000.
★ Estimating
Example 3
Round each number to 1 s.f., calculate in your head, compare with the exact answer. 48 × 21 ≈ 50 × 20 = 1000 — so 10 08 is right and 100.8 is not.

See it

Build a number

Each column is a place; stack blocks with the sliders and read the number, its expanded form and its rounded versions.

Step by step

Worked examples

1

Reading a number

place value

In 60 489.3, what is each digit worth? Write the number in expanded form.

Ask yourself: Start from the units and name the places outwards — the point is the anchor.

Show the solution
  1. Left of the point: 6 ten-thousands, 0 thousands, 4 hundreds, 8 tens, 9 units. Right of the point: 3 tenths.
  2. Expanded form: 60 000 + 400 + 80 + 9 + 0.3.
  3. The 0 matters: without it the 6 would slide into the thousands place and the number would be ten times smaller.

Answer 60 000 + 400 + 80 + 9 + 0.3

2

Rounding three ways

rounding · significant figures

Round 7 846.52 (a) to the nearest hundred, (b) to one decimal place, (c) to one significant figure.

Ask yourself: Which digit do you keep, and which digit decides?

Show the solution
  1. (a) Hundreds place holds 8; next digit 4 → keep: 7 800.
  2. (b) First decimal holds 5; next digit 2 → keep: 7 846.5.
  3. (c) First significant digit 7; next digit 8 → round up: 8 000.

Answer 7 800 · 7 846.5 · 8 000

3

Estimate before you calculate

estimation

A calculator shows 2 971.8 for 62 × 48. Is that believable?

Ask yourself: Round both to one significant figure and multiply in your head.

Show the solution
  1. 62 ≈ 60, 48 ≈ 50, and 60 × 50 = 3 000.
  2. 2 971.8 is close to 3 000 — but a product of two whole numbers cannot end in .8. Something was typed wrong (62 × 47.93 = 2 971.66; 62 × 48 = 2 976).
  3. An estimate catches both wrong magnitudes (29 718) and impossible results.

Answer Roughly right in size, but 62 × 48 = 2 976 exactly — the decimal gives the typo away.

Practice: places, rounding, estimates

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Digit values, rounding to tens, hundreds, decimal places and significant figures, and quick estimates. Your best score is kept in this browser only.

About this lesson

Place value, rounding and estimation for school mathematics: what each digit of a whole number or decimal is worth, how to round to tens, hundreds, one decimal place or one significant figure, and how a quick estimate catches calculation mistakes. A number builder you can move, worked examples and practice questions. Everything on this page runs in your browser; nothing you type is sent or stored. Spotted an error? Tell us.