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How do you convert $150$ to scientific notation ?

seo-qna
Last updated date: 13th Jun 2024
Total views: 373.2k
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Answer
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Hint: In order to write the given question $150$ into its scientific notation then , we need to first understand the term ‘ scientific notation ‘ . Scientific Notation is written in the form of $a \times {10^n}$ , where $1 \leqslant a < 10$ that is we can say the number has a single digit to the left of the decimal point where n is an integer . And the multiplication of a decimal by tens , hundreds and thousands or etc. itself means that the decimal will be moved to the right side by as many as the number of zeroes are there in the multiplier .
If suppose that the decimal number having less digits after the decimal than the multiplier ( or the number of zero is more ) , then the extra zeroes must be added to the final answer as it is . If the decimal is being moved to the right, the exponent will be negative . By following these steps we can find the desired result of writing decimal when multiplying and making it in standard form .

Complete step by step solution:
We have given a number in the form $150$ where there is no decimal . Here, in this question we have to convert into scientific notation by inserting a decimal such that there is only a single digit to the left of the decimal point .
So , to calculate the scientific notation of the given , we have to first just sort that there must be a single digit to the left of the decimal point . Also remember that any number for example – 150 is a number can also be expressed as 150.0 in the form of decimal .
In order to do that we need to move the decimal point to the left side until one digit that 1 comes to the left of the decimal and 5 comes to the right of the decimal point .
Now the decimal point moves two places to the left from $150$ to $1.50$ . But now the multiplier just used 2 zeroes to overcome the decimal and so we can write in scientific notation we have the ${10^2}$ , as we know the fact that states If the decimal is being moved to the left , the exponent will be positive . That is now we have 2 zeros after moving decimal to left and the exponent becomes ${10^2}$ .
Hence , the result is $1.5 \times {10^2}$ as we moved the decimal 2 places to the left .

Note:
1. Do not Forget to verify the end of the result with the zeroes. If you multiply a decimal with 10 , then the decimal point will be moved to the right side by 1 place
2. If you multiply a decimal with 100 , then the decimal point will be moved to the right side by 2 places .
3. If you multiply a decimal with 1000 , then the decimal point will be moved to the right side by 3 places .
4. If the decimal number has less digits after the decimal than the multiplier ( or the number of zero is more ) , then the extra zeroes must be added to the final answer as it is . If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive .
Also remember that any number for example – 150 is a number can also be expressed as 150.0 in the form of decimal .