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Rounding and estimates
Lisa bought a shirt for 299 kronor and pants for 329 kronor. Rounding to the nearest hundred, what is the correct way of estimating the total cost of the purchase?
When you buy several things at the same time, it can be hard to remember and add all the prices in your head. This is why it can be useful to be able to round off numbers. Imagine that you promised to go shopping. You have a shopping list and 60 kronor with you. Do you have enough money?
When we round off numbers, we replace the number with the closest integer, ten, or hundred. We can also round off to tenths or hundredths. In this case, we'll round off the prices to the nearest ten. Let’s take one item at a time. Milk costs 10,50.
If we look at the number line, this is closer to 10 than to 20. We can see that 10,50 is roughly the same as 10 kronor. Bread costs 18,90. If we look at the number line, this is closer to 20 than to 10. 18,90 is roughly equal to 20 kronor.
Eggs cost 23,90. Looking at the number line, we see that this is closer to 20 than to 30 23,90 is then roughly equal to 20 kronor. A rounded number is called an approximate value. When we have rounded the prices, it's easier to add them in your head. 10 + 20 + 20 = 50 kronor We have now done an estimation and calculated roughly how much the items cost.
We have rounded two prices down and one price up to the nearest ten, so they should roughly even out. Therefore, 60 kronor will be enough to pay for the food. If you are still uncertain, you can try rounding the prices to the nearest integer instead, in order to come closer to the exact sum. This can be a little bit more complicated, but we'll try this with the help of the number line again: Milk - 10,50 roughly equal to 11 kronor. Bread - 18,90 roughly equal to 19 kronor.
Eggs - 23,90 roughly equal to 24 kronor. We add them together. 11 + 19 + 24 If we add the tens first, and then the ones, we get 40 + 14 equals 54 kronor. So yes, you have enough money! But hold on, why did we round 10,50 to 11 and not to 10, if 10,50 is right in the middle on the number line?
Well, here are some rounding rules to remember: If the digit after the digit we need to round is 0, 1, 2, 3, or 4, we round down. If the digit after the digit we need to round is 5, 6, 7, 8, or 9, we round up. Now, we have rounded the prices in two different ways and decided that you had enough money. But what happens when you pay? Milk costs 10,50 kronor.
If you had only bought the milk, you would not have been able to pay the exact price. We don't have any 50 öre coins anymore, do we? In this case, the price would have been rounded to the nearest whole number, which is 11 kronor according to the rounding rule, since the following number is 5 and we have to round up. However, you bought more than one item, so the cash register first calculates the exact sum. Only then the sum is rounded to the nearest whole number.
Let’s try a method of writing the numbers to calculate the exact sum: We begin with the tenths, then the ones, and finally the tens. We finish off by placing the decimal comma. The decimal commas should all line up with each other. If the final sum is 53,30, we round to the nearest whole number, which is 53 kronor. Rounding - writing an approximate value of a number.
Remember: Rounding rule: If the digit after the digit we need to round is 0, 1, 2, 3, or 4, we round down. If the digit after the digit we need to round is 5, 6, 7, 8, or 9, we round up. The "wavy" equal sign used with rounding means "approximately equal to". Approximate value - the rounded number. Estimation - when we round numbers before we add them, to make calculations easier.