Rounding Numbers – Part 2

Slideshow 2, Mr Richard Sasaki, Room 307

Objectives

• Understand the meaning of significant figures

• Be able to write large or small numbers in standard index form

• Be able to round and calculate with such numbers

RoundingLet’s have a quick review.

Round the number to…

The nearest 2 decimal places 74.75

The nearest 1 decimal place 74.8

The nearest integer 75

This is a common way to round numbers with decimals. Next we’ll look at rounding with significant figures.

Significant FiguresIf we see a number like 4,458,327,732 it doesn’t look very nice. It may be that some of those digits aren’t very significant so we can simplify it a bit.When we found a number to __ significant figures, we rewrite that number to only show interest in those figures.

Examples

Write 347 rounded to 2 significant figures.350

Write 75,321 rounded to 3 significant figures.

75,300

Significant FiguresWe can also do this with small decimal numbers.

Examples

Write 5.329 rounded to 3 significant figures.5.33

Write 0.00593 rounded to 1 significant figure.

0.006

Any zeroes at the start or end of big or small numbers do not count towards significant digits.

0.0005003(4 s.f)

53,000,000(2 s.f)

Answers

4428,000

430,000400,000

60.00048232

0.0004820.0005

9.392 9.4 948390048000050000027360 27000 30000

837.2 840 80050.00 50 5045.50 45 50100.00 100 100

124000120000100000

Standard FormStandard (index) form comes from index form. If we write a number in index form, we write it in the form…

𝑎𝑏

Writing numbers in standard form is very useful and important for huge or tiny numbers. You will see numbers in this style in physics and social studies too.

But what is it?

Standard FormTo write a number in standard form, we split it into two components.I’ll use the number 741,200,000,000 for the example.

×7.412 1011

This number contains all significant figures. It always has the units figure on the left!

This number is always in the form where is the number of digits –1.

ExamplesLet’s write the following in standard form.

3,500,000,000 3.5

74,000,000,000 7.4

82 8.2

7,530 7.53

0.004 4 0.00392 3.92

Try the worksheet!

Answers

4×103

3.59×104

5×106

4.92×105

3×10−2

8×10− 4

5.79×10− 3

5.43×100

9.43×104

9.65×107

1.5×1069 .75×100

3.12×10− 25.09×10− 4

7×10−41×10− 2

1.496×108

3×108

Answers

300430,000104.30.030.0000430.10.48

7×103

7.3×107

8.42×1033×102

9×103

1.13×108

5.2×103

4.20033×107

9.3×10−8

4×102

6.9×1093.8×10−4

2.163×106

3.1×10− 8