Home

Maths

Number

Rounding: Integers, decimal places, significant figures

Select Lesson

Exam Board

Select an option

Statistics

Sets and Venn diagrams

Sampling and bias

Collecting data: types and classes of data

Mean, median, mode and range

Simple charts and graphs

Pie charts

Scatter graphs

Frequency tables: finding averages

Grouped frequency tables

Box plots - Higher

Cumulative frequency - Higher

Histograms and frequency density - Higher

Interpreting data

Comparing data sets

Probability

Basics of probability

Calculating theoretical probabilities

Probability: Expected and relative frequency

The AND / OR rules

Probability tree diagrams

Conditional probability - Higher

Experimental probability: frequency trees

Trigonometry

Pythagoras' theorem

Sin, cos, tan

Trigonometry: Finding angles and sides

Exact trigonometric values

Sine and cosine rules - Higher

3D Pythagoras - Higher

3D Trigonometry - Higher

Vectors

Vectors - Higher

Angles and geometry

Angles: types, notation and measuring

Basic angle rules

Angles in parallel lines

Circle theorems - Higher

Constructing triangles: SSS, SAS, ASA

Construction: angle and perpendicular bisectors

Construction: Loci

Bearings

Maps and scale drawings

Shapes and area

Properties of 2D shapes

Congruence: conditions for congruent triangles

Similar shapes: Scaling

The four transformations

Area and perimeter: Formulae

Area and circumference of circles: Formulae

3D shapes: faces, edges, vertices

Surface area of 3D shapes: Nets, formulae

Volume of 3D shapes: Formulae

Volume of 3D shapes: Comparing, rates of flow

Area and volume scale factors

Projections and elevations of 3D shapes

Ratio proportion and rates of change

Ratio

Direct and inverse proportion

Finding percentages and percentage change

Compound growth and decay

Converting units: metric and imperial

Converting units: area and volume

Time intervals: converting units of time

Speed, density and pressure: Formulae and units

Graphs

Coordinates and midpoints

Straight line graphs

Drawing straight line graphs

Finding the gradient of a straight line

Equation of a straight line: y = mx + c

Coordinates and ratio

Parallel and perpendicular lines

Quadratic graphs

Reciprocal and cubic graphs

Exponential graphs and circles - Higher

Trigonometric graphs - Higher

Solving equations using graphs

Graph transformations - Higher

Real-life graphs

Distance-time graphs

Velocity-time graphs - Higher

Gradients of real-life graphs - Higher

Algebra

Number

Explainer Video

Tutor: Labib

Summary

Rounding: Integers, decimal places, significant figures

In a nutshell

There are three different types of ways to round numbers. One way of rounding involves rounding to the nearest whole number, ten, hundred, thousand or million. Other ways of rounding include rounding to the nearest decimal place or the nearest significant figure.

Rounding to whole numbers

You can round any number to the nearest whole number, nearest ten, nearest hundred, etc. To round to the nearest whole number, look at the number after the decimal point to see whether to round up or down. To round to the nearest ten, look at the number in the units column to see whether to round up or down.

In the same way, when rounding to the nearest hundred, thousands or millions, look at the digit to the right, or the digit that is one place value lower to see whether to round up or down. If the digit is smaller than five, round down and if the digit is five or bigger, then round up.

Example 1

Round $43.6$ to the nearest whole number.

To round to the nearest whole number, look at the number after the decimal point. As $6$ is bigger than $5$ , round up.

$43.6$ rounded to the nearest whole number is $\underline{44}$ .

Example 2

Round $12 \ 346$ to the nearest hundred.

To round to the nearest hundred, look at the number in the tens column. As $4$ is less than $5$ , round down.

$12 \ 346$ rounded to the nearest hundred is $\underline{12 \ 300}$ .

Decimal places

To round to the nearest decimal place, look at the digit to the right, or the digit that is one place value lower to see whether to round up or down. If the digit is smaller than five, round down and if the digit is five or bigger, then round up.

Example 3

What is the value of $17.342$ to $2$ decimal places?

To round to $2$ decimal places, look at the digit in the $3rd$ decimal place. As $2$ is less than $5$ , round down.

$17.342$ rounded is $\underline{17.34 \ (2 \ d.p.)}$ 

Significant figures

The first significant figure in a number is the first non-zero digit starting from the left. The second significant figure is the digit to the right, then the third significant figure is to the right again, and so on. Zero can be counted as a significant figure from the second significant figure onwards.

Example 3

What is the value of $0.003708$ to $3$ significant figures?

The first significant figure starts at the digit $3$ . The second significant figure is $7$ , and the third significant figure is $0$ . To round to $3$ significant figures, look at the next digit. As $8$ is bigger than $5$ , round up.

$0.003708$ rounded is $\underline{0.00371 \ (3 \ s.f.) }$ 

Learn with Basics

Length:

Rounding decimals

Rounding: Decimal places and significant figures

Jump Ahead