Answer :
Final answer:
To multiply 101 by a two-digit number like 84, multiply 84 by 100 to get 8400, and then add 84 to get 8484. This utilizes the efficiency of multiplication by powers of ten.
Explanation:
To multiply the number 101 by a two-digit number, such as 84, you can use a multiplication shortcut that leverages the properties of powers of ten. This is similar to the method used when multiplying decimals by powers of ten; where you move the decimal point to the right by a number of places equal to the number of zeros in the power of ten.
Using this concept, the multiplication of 101 by 84 can also be thought of as multiplying 84 by 100 and then adding 84 one more time (as 101 is 100+1). Here's the step-by-step explanation:
- Multiply 84 by 100 to get 8400.
- Add the original number 84 to the result of step 1.
- 8400 + 84 gives us the final answer of 8484.
This method is efficient because when you multiply by 100, all you are doing is adding two zeros at the end of the number. It simplifies the calculation because you don't need to perform long multiplication. However, in scientific notation, multiplication and division by powers of ten become even more streamlined. For example, multiplying 9.3 by 107 in scientific notation is simply 9.3 × 107, and the result is written with the coefficient and the exponent of ten.
