---
title: "Place value and estimating: cheat sheet"
subtitle: "Number Foundations"
---

# Place value and estimating

> The words and methods from this unit, with an example of each.

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**power of 10**: Each place value column is a power of 10. The exponent counts the zeros, and the ones column is $10^0 = 1$.

$$10^3 = 10 \times 10 \times 10 = 1000$$

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**expanded notation**: A number as the sum of each digit times its place value. A column holding 0 adds nothing, so leave it out.

$$4052 = 4 \times 10^3 + 5 \times 10^1 + 2 \times 10^0$$

_4052 on the columns: 4 × 10³ + 5 × 10¹ + 2 × 10⁰_

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**decimal places**: The number of digits after the decimal point. To 2 decimal places means to the nearest hundredth.

$$3.746 \text{ has 3 decimal places}$$

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**estimate**: A quick, close answer from rounded numbers. Round to the first digit and keep the size; then compare with the exact answer.

$$38 \times 52 \approx 40 \times 50 = 2000$$

_38 × 52 ≈ 40 × 50 = 2000; the exact answer is 1976_

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**round to decimal places**: Look at the digit straight after the place. 5 or more rounds up; 4 or less leaves the digit. Halfway rounds up.

$$3.746 \to 3.75 \ (2 \text{ d.p.})$$

_3.746 is past the halfway mark 3.745, so it rounds to 3.75_

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**estimating**: Round each number to its first digit, keep its size, calculate, then compare with the exact answer.

$$19.6 \times 4.1 \approx 20 \times 4 = 80$$

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