1.03 Using scientific notation

We will often use our calculator to evaluate expressions with scientific notation. However, knowing our exponent laws we can manipulate calculations that are relatively straightforward or estimate the size of answers for more complex calculations.

Worked example

Use exponent laws to simplify $2\times10^6\times6\times10^5$2×106×6×105. Give your answer in scientific notation.

Think: We could enter this straight into a calculator to solve it, but thinking logically we can break it down into smaller easy steps.

Do: Simplifying first we find:

$2\times10^6\times6\times10^5$2×106×6×105	$=$=	$12\times10^{6+5}$12×106+5
	$=$=	$12\times10^{11}$12×1011

Then we need to adjust our answer to obtain scientific notation, as the first number is larger than ten.

$12$12 can be as expressed as $1.2\times10^1$1.2×101. We will use this to write our answer in scientific notation.

$1.2\times10^1\times10^{11}$1.2×101×1011	$=$=	$1.2\times10^{1+11}$1.2×101+11
	$=$=	$1.2\times10^{12}$1.2×1012

 

Scientific notation and calculators

Calculators will often display numbers in scientific notation but the format may vary between different models. A common variation from showing $2.95\times10^8$2.95×108 is the display $2.95$2.95E$8$8 where the E is for exponent of $10$10. Most calculators will also have a button for entering numbers in scientific notation. This may look like $\times10^x$×10x or like the button EXP circled in blue in the picture. Look carefully at your calculator and ensure you are familiar with the display format and syntax for entering numbers in scientific notation.

 

For example, to write $1.5\times10^9$1.5×109 on this calculator, you would press: 

 

Practice questions

Question 1

Question 2