Question

How do you write the decimal form of \[3.15 \times {10^{ - 8}}\]?

Answer 1

Hint: The numbers can be classified into different types, namely real numbers, natural numbers, whole numbers, rational numbers, and so on. Decimal numbers are among them. Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point. The dot present between the whole number and fractions part is called the decimal point. To write the decimal form of \[3.15 \times {10^{ - 8}}\] we need to move the decimal n places, by adding zeros to it.

Complete step by step solution:
Given,
\[3.15 \times {10^{ - 8}}\]
Determine the exponent n, on the factor 10. Move the decimal n places, adding zeros if needed. If the exponent is positive, move the decimal point n places to the right. If the exponent is negative, move the decimal point |n| places to the left.
\[3.15 \times {10^{ - 8}}\]
The expanded form of 3.15 is:
\[ = 315 \times {10^{ - 2}} \times {10^{ - 8}}\]
Since, the decimal point is after two digits we have the exponent as \[{10^{ - 2}}\] and shifted the terms from \[3.15\] to \[315\], and now combining both the exponents we get:
\[ = 315 \times {10^{ - 10}}\]
As, given the exponent is negative, move the decimal point \[\left| n \right|\]places to the left as here we have the value of n as \[\left| n \right| = \left| { - 8} \right| = 8\] ; the absolute value of -8 is 8 and hence we get:
\[ = 0.0000000315\]

Therefore, the decimal form of \[3.15 \times {10^{ - 8}} = 0.0000000315\].

Note: The place value system is used to define the position of a digit in a number which helps to determine its value. When we write specific numbers, the position of each digit is important. The number of places the decimal point moves is the power of the exponent, because each movement represents a "power of 10" and if any two decimal numbers are multiplied in any order, the product remains the same.