When multiplying and dividing two numbers in scientific notation, why do u sometimes have to rewrite one factor ?

Mathematics

2 answers:

Free_Kalibri [48]2 years ago

8 0

Answer:You have to rewrite it just in case the lead number isn’t a 1 or a 10

Step-by-step explanation:

zalisa [80]2 years ago

5 0

You sometimes need to rewrite a factor because the lead number is not between 1 and 10 as it needs to be in scientific notation. For instance, if we had lead numbers of 2 and 5, as we do in the following problem.

2x10^3 * 5x10^9

Then we get the answer of 10x10^12. We need to adjust this by moving the decimal place and increasing the exponent by 1. The correct answer would be 1x10^13 instead.

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<img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B28%7D%20%2B%20%5Cfrac%7B1%7D%7B70%7D%20%2B%20%5Cfrac%7B1%7D%7B130%7D%20%2B%20

malfutka [58]

Considering the least common multiple of the denominators, it is found that the result of the expression is given by:

$\frac{9100}{138320}$

<h3>How do we add fractions?</h3>

We place all the terms of the addition in "equivalent" fractions, with the same denominator, found from the last common multiple of all the denominators.

In this problem, the denominators are as follows: 28, 70, 130, 208, 304. Using a calculator, their lcm is of 138,320.

Considering equivalent fractions(the numerators are the division of the lcm by the previous denominator), the expression is:

$\frac{4940}{138320} + \frac{1976}{138320} + \frac{1064}{138320} + \frac{665}{138320} + \frac{455}{138320} = \frac{4940 + 1976 + 1064 + 665 + 455}{138320} = \frac{9100}{138320}$