Question

How do you write 417.8 in scientific notation?

Answer 1

Hint: In this question, we need to write 417.8 in scientific notation. For this, we will write it in the form as $ N\times {{10}^{a}} $ where N is a number between 1 and 10, but not 10 itself, a is an integer. In the given number, we will move decimal such that it is in the scientific form. If the decimal is moved to the left by x place we multiply N with $ {{10}^{n}} $ and if the decimal is moved to the right by n place we multiply N with $ {{10}^{-n}} $.

Complete step by step answer:
Here we are given the number 417.8. We need to convert it into scientific notation. For this we need to convert the number into the form $ N\times {{10}^{a}} $ where N is a number lying between 1 and 10, but not 10 itself and a is an integer.
Let us first understand the rule of converting a number of scientific notation.
We first move the decimal point of a number until a new form is a number from 1 to 10 (N) and then we record the exponent (a) as the number of places the decimal point was moved. The power of 10 being positive or negative depends on the direction of movement of the decimal. If the decimal is moved to the right, the exponent is negative and if the decimal is moved to the left, the exponent is positive.
In the number 417.8 as we can see we need to move the decimal left side by two places so that we can get the value of N as 4.178 which lies between 1 and 10. For the power of 10, we will use an as 2 because we moved to 2 places. Since we are moving to the left a will be negative, so our scientific notation looks like this, $ 4.178\times {{10}^{-2}} $.
Hence our required answer is $ 4.178\times {{10}^{-2}} $ .

Note:
Students should carefully write the power of 10 i.e. exponent of 10 taking care of signs. Note that N should always lie between 1 to 10 and it cannot be equal to 10. If it is equal to 10, move decimal one place to left and add 1 to the power of the exponent.