Consider the number thirty-four thousand three hundred. Write this number in standard form.
Before we can write this number in standard form, we must first convert it from words to digits, which we can do using a place value grid. To start with, we have thirty-four thousand. Now this is the same as three lots of 10000 and four lots of 1000. So we have a three in the ten thousands column and a four in the thousands column. We then have 300. So we have a three in the hundreds column, and there are no tens and no units, so zeros in these two columns.
A number is in standard form if it is written as some number 𝑎 multiplied by 10 to the power of 𝑛, where 𝑎 must be greater than or equal to one but less than 10 and 𝑛 is an integer. For numbers greater than one, 𝑛 will be positive. And for numbers less than one, so decimals, 𝑛 will be negative.
We first need to convert 34300 to a number between one and 10. To do so, we can extend our place value table to include tenths and hundredths. And we see that if we move each digit four places to the right, then we get the number 3.43, which is between one and 10. So in standard form, the number 34300 will be 3.43 multiplied by 10 to some power, which we now need to work out.
To go back the other way, so that’s to get from the number 3.43 to the number 34300, we need to move each digit four places to the left. This means that we’d need to multiply the decimal by 10 four times. And multiplying by 10 four times is the same as multiplying by 10 to the power of four. So the power of 10 that we need in our answer in standard form is four. In standard form then, the number 34300 is 3.43 times 10 to the power of four.