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Math  /  Numbers & Operations

QuestionAccording to the video, how many nanoseconds are in a millisecond?
Choose the correct answer below. A. 1,000,0001,000,000 B. 1,000 C. 100,000 D. 10,000

Studdy Solution

STEP 1

What is this asking? How many nanoseconds equal one millisecond? Watch out! Prefixes can be tricky!
Don't mix up the meanings of "nano" and "milli."

STEP 2

1. Milliseconds to seconds
2. Seconds to nanoseconds
3. Combine!

STEP 3

The prefix "milli" means one-thousandth.
So, one millisecond is one-thousandth of a second!
We can write this as a fraction: 1 millisecond=11000 seconds1 \text{ millisecond} = \frac{1}{1000} \text{ seconds}

STEP 4

"Nano" is super-tiny!
It means one-billionth.
So, one nanosecond is a billionth of a second!
As a fraction: 1 nanosecond=11,000,000,000 seconds1 \text{ nanosecond} = \frac{1}{1,000,000,000} \text{ seconds}

STEP 5

Let's flip that fraction to find out how many nanoseconds are in one second.
If one nanosecond is one-billionth of a second, then one second is one billion nanoseconds! 1 second=1,000,000,000 nanoseconds1 \text{ second} = 1,000,000,000 \text{ nanoseconds}

STEP 6

We know how many seconds are in a millisecond, and we know how many nanoseconds are in a second.
Let's put them together!
We want to convert 11 millisecond to nanoseconds. 1 millisecond=11000 seconds1 \text{ millisecond} = \frac{1}{1000} \text{ seconds} 1 second=1,000,000,000 nanoseconds1 \text{ second} = 1,000,000,000 \text{ nanoseconds}So, we can substitute the **nanosecond equivalent of one second** into the **millisecond to seconds** equation: 1 millisecond=11000⋅1,000,000,000 nanoseconds1 \text{ millisecond} = \frac{1}{1000} \cdot 1,000,000,000 \text{ nanoseconds}

STEP 7

Now, let's do some arithmetic!
We're multiplying a fraction by a whole number, which is the same as dividing the whole number by the denominator of the fraction. 1 millisecond=1,000,000,0001000 nanoseconds1 \text{ millisecond} = \frac{1,000,000,000}{1000} \text{ nanoseconds} Dividing 1,000,000,0001,000,000,000 by 10001000 is like canceling out three zeros. 1 millisecond=1,000,000 nanoseconds1 \text{ millisecond} = 1,000,000 \text{ nanoseconds}

STEP 8

There are **1,000,000** nanoseconds in a millisecond.
That's answer A!

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