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Question

Which is the correct relation for the numbers 3.28×107 and 4.59×105, written in scientific notation?

A
4.59×105>3.28×107
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B
4.59×105<3.28×107
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C
4.59×105=3.28×107
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D
Cannot be determined
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Solution

The correct option is B 4.59×105<3.28×107
First Method:––––––––––––––––

Step 1:
Write the numbers in scientific notation. Here, 3.28×107 and 4.59×105 are already in scientific notation.

Step 2:
Compare the exponents of numbers. The larger the exponent, the greater the number.
7>5
3.28×107>4.59×105

Second Method:––––––––––––––––––

We can compare the numbers by making the same exponent to the base 10.

In 4.59×105, to convert the exponent of 10 as 7, we need to multiply 102 with 105. And, we can achieve that by moving the decimal point in 004.59 by 2 units to the left.

Making the powers of 10 as 7 for both the numbers:
3.28×107 and 4.59×105=0.0459×107

The number with the larger coefficient is greater.

3.28>0.0459
3.28×107>0.0459×107

Hence, the correct comparsion between the numbers 3.28×107 and 4.59×105 would be 4.59×105<3.28×107––––––––––––––––––––––––.

Therefore, option (b.) is the correct one.

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