Final answer:
To maintain equality in an equation when dividing, the dividend must be multiplied by the same power of 10 as the divisor. This simplifies the process and aids in converting to scientific notation, making the arithmetic operation easier to perform.
Step-by-step explanation:
When performing division with numbers in scientific notation or dealing with decimals and powers of 10, it's important to maintain the balance of the equation. If you multiply the divisor (the number you are dividing by) by a power of 10, you must also multiply the dividend (the number being divided) by the same power of 10 to keep the equation equivalent. This method maintains the equality of the equation and helps simplify calculations, particularly when converting to scientific notation.
For example, if you start with the equation 1.9436 ÷ 10, to simplify, you could multiply both the dividend and divisor by 10. This would effectively shift the decimal point two places to the right in the dividend, making it easier to see that 1.9436 ÷ 10 is equal to 0.19436.
In scientific calculations, using shorthand notation for powers of 10 significantly eases the process of multiplication and division. For instance, when multiplying two numbers in scientific notation like (3 × 10⁵) × (2 × 10⁰), you just multiply the coefficients (3 and 2) and add up the exponents of 10 to obtain the result, which is 6 × 10¹⁴. This technique vastly simplifies dealing with large numbers.