Rounding and Significant Figures

Grade 4

What rounding actually does

Rounding is about choosing the nearest "tidy" number at a given level of precision. You've probably rounded to decimal places before — the same logic applies to significant figures, which is just a different way of deciding where to stop.

The common slip is to look at the wrong digit when deciding whether to round up or down. One rule, remembered properly, sorts it every time.

Look at the digit one place to the right of where you're rounding. If it's 5 or more, round up the digit you're keeping. If it's 4 or less, leave that digit alone.

Rounding to decimal places

Decimal places (d.p.) count how many digits you keep after the decimal point. To round to 2 d.p., look at the third decimal place and apply the rule.

EXAMPLE
Round 7.3862 to 2 decimal places.
The second decimal place is 8. The third decimal place is 6 — that's 5 or more, so round up: 7.38 becomes 7.39.
EXAMPLE
Round 4.1749 to 1 decimal place.
The first decimal place is 1. The second is 7 — that's 5 or more, so round up: 4.2.

Significant figures

Significant figures count digits starting from the first non-zero digit of the number — whether that's before or after the decimal point. So 0.00471 has three significant figures (4, 7, 1), and 30 200 could have 3 or 5 depending on context.

To round to a given number of significant figures, identify the digit in that position and apply exactly the same rule: look one place to the right.

EXAMPLE
Round 0.082 647 to 3 significant figures.
The first significant figure is 8 (the zeros before it don't count). Counting three significant figures gives 8, 2, 6. The next digit is 4 — that's 4 or less, so leave the 6 alone: 0.0826.
Don't start counting from the decimal point or the first digit of the whole number — always start from the first non-zero digit. That's the first significant figure.

One thing to watch with zeros

When rounding a whole number, you must replace the removed digits with zeros to keep the right size. Rounding 58 430 to 2 significant figures gives 58 000 — not 58. The zeros are there to hold the place value, not as significant figures.

Nova
Try this one

A formula used in physics is:

\[ T = \frac{x^2 + y^2}{w} \]

where \( x = 14.6 \) (measured to 3 significant figures), \( y = 9.3 \) (measured to 2 significant figures) and \( w = 52 \) (measured to the nearest integer).

Calculate the upper bound for \( T \). Give your answer to 3 significant figures. [3]

Nova's hint:

This is about finding the upper bound of a formula involving multiple measurements with different levels of accuracy.

Ask yourself: 'which combination of bounds for each variable gives the largest possible value of the formula?' For a fraction, the upper bound comes from making the numerator as large as possible and the denominator as small as possible. Identify the bounds of each variable separately first.

Try to Solve it with Nova?