Video: Writing a Decimal in Standard Form

Write this decimal in standard form: (9 × 10) + (5 × 1) + (3 × 0.1) + (2 × 0.01) + (7 × 0.0001).

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Video Transcript

Write this decimal in standard form. Nine multiplied by 10 plus five multiplied by one plus three multiplied by 0.1 plus two multiplied by 0.01 plus seven multiplied by 0.0001.

So what we can see here is that our decimal has been deconstructed into five different parts. So what we need to do is put this all back together to put it into its standard decimal form. So, in order to do that, what we’re gonna do is calculate each of the parts separately. So first of all, what we have is nine multiplied by 10 which is equal to 90. Then we have five multiplied by one which is equal to five.

So next we have one which is slightly more challenging. Cause we got three multiplied by 0.1. Well, three multiplied by 0.1 is equal to 0.3. And that’s because if we have three multiplied by 0.1, well, then this is the same as three multiplied by a tenth. Well, three multiplied by a tenth is three-tenths, which is the same as 0.3.

Okay, great. So now let’s move on to the next one. Well, in the same way, but this time looking at hundredths, we’ve got two multiplied by 0.01. Well, this is equal to 0.02 because what this would be is two multiplied by one hundredth, which is the same as two hundredths, which is the same as 0.02. So then, next, what we have is seven multiplied by 0.0001, which is equal to 0.0007. Cause it’s the same as seven multiplied by — and then what we’ve got here is ten thousandths. So that’s gonna give us seven ten thousandths, which is 0.007 [0.0007].

At this point, it’s worth pointing out a common mistake. So we’ve got a question like this. So we’ve gone from tens to units to tenths to hundredths. It could be quite easy to think, well, the next one is got to be thousandths and actually misread it, and misread it as two zeros not three zeros after the decimal point. So be very careful when looking at that to see how many numbers or how many digits are after the decimal point, most specifically the number of zeros.

So now what we’ve got is our decimal which is 90 plus five plus 0.3 plus 0.02 plus 0.0007. Well, there are a few different methods we could use to add this up, but the one that we’re gonna use in this question is the column-addition method. So, in order to set up a column addition, what I’ve done is set up our columns for our place values. So we’ve got tens, units, then we’ve got our decimal point, tenths, hundredths, thousandths, then ten thousandths.

So what I’ve done is I’ve put in our first value, which is 90. However, it is also a good trick to actually add in zeroes after to fill the other place values. And the reason we do that is to keep everything aligned. And we know that we need place values up to one over 10000 or one ten thousandth. And that’s because we’ve got one of our values as 0.0007, which we’ve already said is seven ten thousandths.

So that’s our 90 in our column addition. Next, we move on to five, which means we put five in the units column and then our decimal and then four zeros in the other empty columns. Then we have 0.3, so we put a three in the tenths column and then the rest as zeros. Then we have 0.02, so we put two in the hundredths column and then the rest as zeros. Then, finally, we have 0.0007, so we put seven in the ten thousandths column.

And, like I said, be careful here to make sure that it goes in the right column and is ten thousandths not thousandths. Cause, as you can see, our thousandths column has zero all the way down. And that’s because none of the values that we’re adding were thousandths. So then what we do is we add our horizontal line and our addition sign.

And now the next stage is just to add up each of our columns. So in the ten thousandths column, we’ve just got seven. And then, as we’ve already said, in the thousandths column, we’ve got zero, two in the hundredths column, three in the tenths column, our decimal point which is all aligned, five in the units column, and then finally nine in our tens column. So, therefore, we can say that the decimal in the question when written in standard decimal form is 95.3207.

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