Question

How many milliseconds are in $$6.7$$ seconds?

Answer 1

Hint: Here, we will use the concept of conversion of units. Both milliseconds and seconds are units of time and second is a larger unit than a milliseconds. We will convert the given time in decimal into a fraction. Then we will convert the given quantity from one unit to another unit by multiplying the converting factor to it.

Formula Used:
1 Second is equal to 1000 milliseconds i.e., 1 Second $$=$$ 1000 milliseconds.

Complete Step by Step Solution:
We are given that $$6.7$$ seconds.
Now, we will convert the given seconds in the form of decimals into a fraction, we get
$$6.7s={\displaystyle \frac{67}{10}}s$$
We know that 1 Second is equal to 1000 milliseconds i.e., 1 Second $$=$$ 1000 milliseconds.
Now, we will find the milliseconds in the given seconds by multiplying the given seconds with 1000 to convert into milliseconds.
$$\Rightarrow 6.7s={\displaystyle \frac{67}{10}}\times 1000ms$$
Now, by cancelling out the factor, we get
$$\Rightarrow 6.7s=67\times 100ms$$
Now, by simplifying, we get
$$\Rightarrow 6.7s=6700ms$$

Therefore, the milliseconds in $$6.7$$ seconds is 6700 milliseconds.

Additional Information:
While converting a decimal into a fraction, we will rewrite the decimal as a fraction by writing the decimal number as the numerator and the number 1 as the denominator. Then we will multiply the numerator and the denominator by the number 10 raised to the power of $$n$$ where $$n$$ is the number of digits after the decimal point.

Note:
We know that a millisecond is defined as a unit of time representing$${\displaystyle \frac{1}{1000}}$$ of a second. It is denoted by the symbol $$ms$$. A second is defined as a unit of time representing$${\displaystyle \frac{1}{60}}$$ of a minute. It is denoted by the symbol $$s$$. Whenever the conversion is made from the smaller unit into the larger unit, then the common factor has to be divided whereas the conversion is made from the larger unit into the smaller unit, then the common factor has to be multiplied. This is common for all the conversion of SI units. These units should be remembered in finding the ratios and proportion of similar quantities.