A number rounds to 8.2. The sum of the digits is 13. The product of the digits is 48. What is the number?
The number is 8.23
You just have to think about it like this
if it's rounded to 8.2 either the first two numbers are 8.2 or the 8.1 since it has to round to .2 the numbers before it can be bewteen .0 - .4 to make it stay .2 or .5 -.9.
Now at the same time think what can we multiply with 8x1 to get 48? 6 right, but then the sum of 13 isn't satisfied.
so that means 8.1 doesn't work
so now try 8x2, what you you multiply with 8x2 (=16) to get 48?
3 right?
now let's see if all the criteria is satisfied. 8.23 rounds to 8.2, it adds up to 13, and it multiplies to 48. So it does satisfy it.
If you are wondering why only one more number was added it's because of the whole rounding thing. When you round you usually only look one place to the right so it isn't necessary to go any further past the hundreths place in this case.
0.3 + { - 1 .2 ]
To find the number, let's break down the information provided step by step.
First, we know that the number rounds to 8.2. This means that the digit in the tenths place is 2 and the digit in the ones place is 8. The number could be something like 8.24 or 8.25, but we don't have enough information to determine the precise decimal value. So, let's focus on finding the value of the whole number.
Next, we are told that the sum of the digits is 13. To find the whole number, we need to find the missing digit(s) which should add up to 13 when combined with 8 and 2.
Let's make a list of all the possible combinations of digits that add up to 13, based on the condition that the number is rounded to 8.2:
1 + 4 + 8 = 13
2 + 3 + 8 = 13
3 + 2 + 8 = 13
4 + 1 + 8 = 13
Now, we are given another clue that the product of the digits is 48. From the above combinations, let's calculate the product of the digits for each one:
1 × 4 × 8 = 32
2 × 3 × 8 = 48
3 × 2 × 8 = 48
4 × 1 × 8 = 32
Based on the condition that the product is 48, we can eliminate the combinations that do not fulfill this requirement. In this case, we can eliminate the combinations with a product of 32. Therefore, the possible combinations that meet all the given conditions are:
2 + 3 + 8 = 13
3 + 2 + 8 = 13
Now, let's focus on finding the value of the whole number. Since the number rounds to 8.2, we know that the digit in the tens place must be either 2 or 3.
If the tens digit is 2, the number would be 28.2. However, the sum of the digits would be 10, not 13, so this is not possible.
Therefore, the only remaining possibility is that the tens digit is 3. In this case, the number would be 38.2. And indeed, the sum of the digits (3 + 8 + 2) is 13, and the product of the digits (3 × 8 × 2) is 48.
Hence, the number is 38.2.