## 14.6 Estimate mass

**Mass:** Mass is a measure of how much matter is there in an object. Mass is usually measured by weight. The object with greater weight is considered as having the greater mass.

### 14.6.1 Mass, Grams, and Kilograms

The units of mass are the same as the units of weighs. The units of mass are grams, kilograms, pounds.**Grams:** The basic unit of mass in grams. We write it as ‘g’.**Pounds:** The unit of mass in the FPS system is pounds.**Kilograms:** The 1000 grams together are called 1 kilogram. We write it as ‘kgs.’

**Use Reasoning to Estimate Mass:**

James and Robert estimated the mass of an apple. James’s estimate is 300 grams. Robert’s estimate is 2 kilograms. Which is the better estimate of the mass of an apple?

Mass is a measure of the amount of matter in an object. Grams and kilograms are two metric units of mass.

**Step 1**

Use known masses and the table to compare grams to kilograms. Select the unit that will give a better estimate.

The apple is smaller than the watermelon. A kilogram is too large of a unit to estimate the mass of the apple.

The grape is smaller than the apple. Grams are smaller units that can be used to estimate the mass of the apple.

**Step 2**

Use a pan balance to find the mass of apple. Then evaluate James’s estimate

The apple has a mass of 278 grams.

300 grams is close to 278 grams. James’s estimate is reasonable.

300 grams is a better estimate than 2 kilograms.

**Example1: **Choose the better estimate for each:

**Answers: **(a) 3 grams is a better estimate than 5 kilograms.

(b) 5 kilograms is a better estimate than 40 grams.

### 14.6.2 Conversions

For the conversion of kg to grams, we simply multiply the quantity by 1000. For the conversion of grams to kg, we divide it by 1000.

For the conversion of pounds to grams, we simply multiply the quantity by 454. For the conversion of pounds to grams, we divide it by 454.

**14.7 Measure Mass**

### 14.7.1 Measuring of Mass

There are many different instruments for measuring mass. Some of them are beam balance, digital balance, common balance and so on. The concept of measuring the mass is by comparing the unknown with the known quantities.

The above figure shows a common balance. The left balance is for the unknown weights, and the right balance is for the known weights. The balance bends to the heavier side. If the two balances are at the same level, that implies both masses are the same.

### How do you measure mass?

A. A pan balance with gram and kilogram weights can be used to find the mass of an object.

What is the mass of a box of chocolates?

When measuring mass, it is important to be precise. Use grams, kilograms, or both to find an exact measure.

B. Place the box on one pan. Place enough gram and kilogram weights on other pan so the pans balance.

C. The box balances with one 1-kilogram weight, two 100-gram weights, and four 10-gram weights.

So, the mass of the box is 1 kilogram 240 grams or 1,240 grams.

Write the larger unit before the smaller unit when recording measurements.

### Example:

Write the total mass represented in each picture.

**Answers:** (a) 6 kg (b) 931 g

### 14.8 Solve word problems involving Mass and Liquid Volume

In this section, we solve problems involving capacity as well as mass.

**Example:** 5 kg of lemons make 2 L of lime juice. How much mass of lemons is required to make 10 L of lime juice?

**Solution:** 2 L of lime juice requires 5 kg of lemons

2 x 5 = 10 L of lime juice requires 5 x 5 = 25 kgs of lemons

### 14.8.1 Word problems involving mass

**Example:** Jacob bought 7 boxes of chocolates, each having a mass of 125 g. How much mass of chocolates did he buy?

**Solution:** Each box has a mass of 125 g, and Jacob bought 7 such boxes. The total mass would be 7 times of 125, i.e., 875 g or 0.875 kg

## Exercise:

- What is the sum of the masses 1.135 kg and 1365 g?
- David bought 4.4 pounds of apples. What weight did he buy? (Round the value to the nearest integer).
- Thomas, a book storekeeper, have 5 shelves, and each shelf holds 7 books. The mass of each book is 235 g. How much mass do the 5 shelves hold? (In kg)
- Convert 5 pounds to kg.
- Compare the weights given below and arrange them in increasing order.

3 pounds, 5.24 kg, 5420 g, 542 g

### What we have learned:

- The concept of mass (Definition and units)
- Different units of mass
- Conversions of units of mass
- Problems on mass

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