Final answer:
Forty-six and nine tenths are written as the decimal number 46.9. Decimal points move when multiplying or dividing by powers of ten, which is also a fundamental part of understanding scientific notation.
Step-by-step explanation:
To write forty-six and nine tenths as a decimal number, you place the whole number before the decimal point and the tenths value after the decimal point. Therefore, forty-six and nine tenths is written as 46.9. This is because the whole number part is 'forty-six' and the tenths part is 'nine tenths', which translates to 9 in the first decimal place.
When we multiply or divide decimals by powers of ten, the decimal point moves to the right or left respectively. For example, to multiply a number like 1.9436 by powers of 10, such as 10, 100, or 1000, we move the decimal point one, two, or three places to the right, resulting in 19.436, 194.36, and 1943.6 respectively. Conversely, to divide by powers of ten, we move the decimal point to the left.
Adjusting decimal numbers with powers of ten is a common operation in math and is an important concept in scientific notation. For example, to express the number 965 in scientific notation, we transform it to 9.65 and then denote the change by attaching an exponent, resulting in 9.65 × 10². Scientific notation is also used for very small numbers, such as representing 0.0000045 as 4.5 × 10⁻⁶.