Standard index form problems. Solving problems in standard form.

In this article I will show you how you can solve harder problems involving numbers in standard index form. Make sure you know how to write numbers in standard index form before you start. One of the best ways to solve standard index form problems is to first convert your numbers into ordinary numbers, work out the calculation and then change your answer back into standard form.  Let’s take a look at some examples.

Example 1

Work out 3.76 × 10⁵ + 1.8 × 10⁴. Write your final answer in standard form.

First write 3.76 × 10⁵ and 1.8 × 10⁴ as normal numbers.

3.76 × 10⁵ = 376000          (multiply 3.76 by ten 5 times)

1.8 × 10⁴ = 18000               (multiply 1.8 by ten 4 times)

Now you can add together these numbers (do this using the carrying method or in your head):

376000 + 18000 = 394000

Now convert this answer back into standard form = 3.94 × 10⁵.

Example 2

Work you 3.2 × 10⁷ ×  4 × 10⁵

Again write 3.2 × 10⁷ ×  4 × 10⁵ as normal numbers.

3.2 × 10⁷ = 32000000

4 × 10⁵ = 400000

Now multiply these two numbers together. The easiest way to do this is to ignore the zeros and add them on at the end.

32 × 4 = 128

So 32000000 × 400000 = 12800000000000

Now all you need to do now is change this answer into standard index form.

This gives 1.28 × 10^13

Example 3

Work out 2.9 × 10⁶ – 1.34 × 10⁶.

Again if you change both numbers into standard index form you get 2900000 and 1340000.

Now all you have to do next is take these number away. Do this using the borrowing method.

2900000 – 1340000 = 1560000.

Now converting 1560000 back into a standard index form number you get an answer of 1.56 × 10⁶.

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